Review - Sections 4.1 4.2 4.3 and 4.4 Review Theory...

Sections 4.1, 4.2, 4.3, and 4.4: Review TheoryInstructor: Ms. Hoa Nguyen([email protected])4.1Critical NumbersTo ﬁnd critical numbers of a functionf:- 1. Find the derivativef0(x).- 2. Find the critical numbersin the domain offby considering 2 cases:f0(x) = 0 andf0(x)does not exist.The Closed Interval MethodTo ﬁnd the ABSOLUTE maximum and minimum values of a continuous function f on aclosedinterval[a,b], do the following steps:- 1. Find the critical numbersin() and their f-values.- 2. Find the values offat the endpointsof the interval.- 3. Compare the f-values: The largest value from steps 1 and 2 is the absolute maximum value.The smallest is the absolute minimum value.Local Maximum or MinimumGiven a graph of a functionfon its domainD, to know iffhas a LOCAL max or min atx=c,ﬁrst we pick an open intervalcontainingcandlying inside the domainD.- If wecannotpick such an interval,fdoesnothave local max or min atx=c. This meansthatfNEVER has local max or min at the endpoints of the domainD.

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